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The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.

Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.

"Infinite Curl 7," by Matjuska Teja Krasek in collaboration with Dr. Clifford Pickover (2006)Digital print, 9.9" x 10.1". Kraskek's interest is focused on the shapes' inner relations, on the relations between the shapes and between them and a regular pentagon. Her artworks also illustrate properties such as golden mean relations, self similarity, ten- and fivefold symmetry, Fibonacci sequence, inward infinity and perceptual ambiguity. She employs contemporary computer technology as well as classical painting techniques.

"The image represents the behavior of mathematical feedback loops, and more particularly the iteration of a complex function. The figure is our rendition of a visually interesting quartic variant of a Ushiki Phoenix Julia set. As with other fractals, the image exhibits a wealth of detail upon successive magnifications. The image �Infinite Curl 7� has been made in collaboration with Dr. Clifford Pickover, the author of more than thirty books about mathematics, art, and science." --- Matjuska Teja Krasek, Freelance artist, Ljubljana, Slovenia, EU Apr 28, 2009

"Flow 4," by Elizabeth Whiteley (2008)Museum board and acrylic paint, 7.5" x 13.5" x 10.5". "'Flow 4' is created by the close proximity of two Golden Triangles (base angles of 72 degrees and vertex angle 36 degrees). The plane of each triangle is curved in opposing directions to create an aesthetically pleasing form. The sculpture changes our perception of a static and planar geometric shape and makes for a dynamic visual experience. The curves move the eye around the form and suggest multiple points of view." --- Elizabeth Whiteley, Studio artist, Washington, DCApr 14, 2009

"Flow 1," by Elizabeth Whiteley (2008)Laminated canvas and acrylic paint, 7.5" x 14" x 7.5". "'Flow 1' is created by intersecting two Golden Triangles (base angles of 72 degrees and vertex angle 36 degrees). The plane of each triangle is partially bisected and then curved to create an aesthetically pleasing form. One triangle is smooth; the other has a textured surface. The sculpture changes our perception of a static and planar geometric shape and makes for a dynamic visual experience. The curves move the eye around the form and suggest multiple points of view." --- Elizabeth Whiteley, Studio artist, Washington, DCApr 14, 2009

"A Pattern of 48 Different Squares," by Anna Viragvolgyi (2008)Digital print, 20" x 20". "This is a pattern of the 48 different squares, where the square sheets are striped diagonally, the stripes are colored by three colors such that the adjacent stripes are different color. Albeit the arrangement of the squares is not regular, since all the elements are different, the whole surface is symmetrical. Changing the neighborhoods of the elements engenders a different shape. There are innumerable patterns possible. (For example rectangles may be made--with matching opposite borders--which form tori.) The almost limitless solution patterns enhance cognitive skills." --- Anna Viragvolgyi, Mathematician, Budapest, HungaryApr 14, 2009

"Monge's Theorem," by Sumon Vaze, King George V School, Hong Kong (2008)Acrylic on Canvas, 18" x 24". "The external tangents to three circles, taken in pairs, meet at three points, which are collinear. I seek to depict interesting mathematical truths, curiosities and puzzles in simple, visually descriptive ways. Mathematical amusements inspire the color and form in my paintings, and I try to strike a balance between the simplicity of the concepts and their depiction in art." --- Sumon Vaze, High School Teacher of Mathematics, King George V School, English Schools Foundation, Hong KongApr 14, 2009

"Swarming Pentaplex," by Paul Stacy (2004)Giclee print on canvas (mounted) scanned from original artwork, acrylic paint on board, 20" x 20". "'Swarming Pentaplex' is a representation of the seven Penrose rhomb vertex groups, which I inadvertently "discovered" while experimenting with various matching rules. Of course the Penrose vertex groups have been long-known, however this exploded arrangement results from a very simple underlying tile decoration, with a gradual feathering out of the basic pattern. The resultant picture has great beauty inherent to pentagonal geometry with its aesthetic revelations of the "golden mean". The title refers to the fact that in the right half-light and standing at the right distance the painting comes alive with movement in waves across the canvas, like swarming bees! " --- Paul Stacy, Landscape Architect, Sydney, New South Wales, AustraliaApr 14, 2009

"Fractaled Fire," by Christopher Shaver, Rockhurst University, Kansas City, MO (2008)Digital photography, 11" x 14". "This work is a collage of photos taken during the fireworks display at Fair St. Louis on July 4, 2008. Each firework is somewhat self-similar and recursive in nature, with a common pattern appearing at both the center and the outer edges, and each piece having almost the same appearance. The shape is complex even on a small scale. The dimension of a firework is difficult to comprehend since its shape is constantly changing over time, but is a three-dimensional display. The change over time can be viewed and even is part of the overall image because of the appearance of the smoke left behind in the same shape as the colored flame. These art pieces are the product of a student research project I was a part of, exploring the relationship between art and math by a study of fractals." --- Christopher Shaver, Student, Department of Mathematics and Physics, Rockhurst University, Kansas City, MOApr 14, 2009

"Chinese Button Knot," by Carlo H. Sequin, University of California, Berkeley (2007)Bronze, 8" tall. "The Chinese Button Knot is a nine-crossing knot, number 9-40 in the knot table. It actually has more symmetries than one would infer from the usual depiction in these tables. This has been brought out in this 3D sculpture, which has one 3-fold and three 2-fold rotational symmetry axes. It has been implemented as an alternating over-under path on the surface of a sphere, realized by a ribbon of continuous negative Gaussian curvature." --- Carlo H. Sequin, Professor of Computer Science, EECS Computer Science Division, University of California, BerkeleyApr 14, 2009

"Equinox," by Anna Ursyn, University of Northern Colorado, Greeley (2008)Fortran, photosilkscreens, photolithographs, photographs, etc., 8" x 10". "I explore dynamic factor of line. I find computers to be a perfect tool to explore the regularity of nature. I use the computer on different levels. First I draw abstract geometric designs for executing my computer programs. Then I add photographic content using scanners and digital cameras. The programs that produce two-dimensional artwork serve as a point of departure for photolithographs and photo silkscreened prints on canvas and paper. All of these approaches are combined for image creation with the use of painterly markings." --- Anna Ursyn, Professor, University of Northern Colorado, GreeleyApr 14, 2009

"Figure-8 Knot," by Carlo H. Sequin, University of California, Berkeley (2007)Second Prize, 2009 Mathematical Art Exhibit. Bronze, 9" tall. "The Figure-8 Knot is the second simplest knot, which can be drawn in the plane with as few as four crossings. When embedded in 3D space it makes a nice constructivist sculpture. This particular realization has been modeled as a B-spline along which a crescent-shaped cross section has been swept. The orientation of the cross section has been chosen to form a continuous surface of negative Gaussian curvature." --- Carlo H. Sequin, Professor of Computer Science, EECS Computer Science Division, University of California, BerkeleyApr 14, 2009

"Universe Before Big Bang," by Clifford Singer, Clark County School District, Las Vegas, NV copyright 1989Acrylic on plexiglass, relief, 36" x 36" x 2". "This painting as a model entitled, Universe Before Big Bang, 1989, is intended to reconstruct the universe prior to the Big Bang. My concept in 1989 was to take a snapshot of the universe encapsulated in a non-Euclidean square. Thus, matter is then present before the Big Bang. Origins of the cosmos are found in supersymmetries and further understanding of concepts for their elucidation. As an artist and geometer 'infinity' has taken an important place in my life in terms of abstraction. My art combines both ancient and modern mathematical foundations ranging from Pythagoras to Einstein." --- Clifford Singer, Artist/Fine Art Teacher, Clark County School District, Las Vegas, NVApr 14, 2009

"Star Birth," by Nathan Selikoff (2007)Lightjet print, 24" x 18". "Underlying this artwork is a two-dimensional plot of the 'typical behavior' of a chaotic dynamical system, a strange attractor. The base image is computed with a set of iterated functions, which serve as a numerical approximation to integrating the underlying differential equations. The iterated functions contain four coefficients, which are controlled by sliders in interactive custom software and control the appearance of the attractor. Once the particular form is chosen, it is rendered as a high-resolution 16-bit grayscale image, colorized using gradient mapping and edited to enhance contrast, control composition, and add special effects. I love experimenting in the fuzzy overlap between art, mathematics, and programming. The computer is my canvas, and this is algorithmic artwork--a partnership mediated not by the brush or pencil but by the shared language of software. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork." --- Nathan Selikoff, Artist, Orlando, FLApr 14, 2009

"Chinese Dragon," by Nathan Selikoff (2007)Lightjet print, 18" x 24". "Underlying this artwork is a two-dimensional plot of the 'typical behavior' of a chaotic dynamical system, a strange attractor. The base image is computed with a set of iterated functions, which serve as a numerical approximation to integrating the underlying differential equations. The iterated functions contain four coefficients, which are controlled by sliders in interactive custom software and control the appearance of the attractor. Once the particular form is chosen, it is rendered as a high-resolution 16-bit grayscale image, colorized using gradient mapping and edited to enhance contrast, control composition, and add special effects. I love experimenting in the fuzzy overlap between art, mathematics, and programming. The computer is my canvas, and this is algorithmic artwork--a partnership mediated not by the brush or pencil but by the shared language of software. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork. " --- Nathan Selikoff, Artist, Orlando, FLApr 14, 2009